Why Do Bounded Mediums Have Specific Eigenfrequencies?

[saumya yadav]

in waves and oscillations i read that any bounded medium oscillates in a particular freuency...why is it so?i need a proper reason for this

 

[mfb]

Please post your questions in new threads, not in existing threads about other topics. I splitted the thread.

Two arguments:
- you can perform a Fourier transformation on any oscillation, and you get a set of some resonance frequencies.
- every oscillation returns to its initial state eventually (not exactly true, but good enough here). Afterwards, it just repeats again and again, if you neglect damping.

 

[saumya yadav]

what gives rise to these oscillations?thermal energy of constituting particles...?I guess.

 

[nasu]

what gives rise to these oscillations?thermal energy of constituting particles...?I guess.

This may indicate that there is some confusion regarding the meaning of
"any bounded medium oscillates in a particular frequency"

"Oscillates" here does not mean that it spontaneously oscillates.
If you "excite" the medium somehow, this will induce oscillations (or waves).

 

[PJC01]

The existence of eigenfrequencies in waves and oscillations is a fundamental property of any bounded medium. This phenomenon is a result of the medium's inherent physical properties and the way it responds to external forces.

To understand why a bounded medium oscillates at a particular frequency, we need to consider the concept of resonance. When an external force is applied to a medium, it causes the particles within the medium to vibrate. These vibrations propagate as waves through the medium and can have a wide range of frequencies.

However, when the frequency of the external force matches the natural or eigenfrequency of the medium, a phenomenon known as resonance occurs. In resonance, the amplitude of the vibrations increases significantly, resulting in a sustained oscillation at that particular frequency.

This can be explained by the fact that when the external force matches the eigenfrequency, it is in phase with the natural vibrations of the medium. This means that the force reinforces and adds to the existing vibrations, resulting in a larger amplitude.

Moreover, the bounded nature of the medium also plays a crucial role in determining its eigenfrequencies. The boundaries of a medium act as constraints, causing the waves to reflect and interfere with each other. This interference creates standing waves, which have distinct eigenfrequencies depending on the size and shape of the medium.

In summary, the existence of eigenfrequencies in waves and oscillations is a result of the resonance phenomenon and the bounded nature of the medium. These frequencies are unique to each medium and are determined by its physical properties and boundaries.